Probably no department of Analytical Mechanics presents greater difficulties than that which treats of the motions of fluids; and hitherto the success of mathematicians therein has been comparatively limited. In the theory of the waves, as presented by MM. Poisson and Cauchy, and in that of sound, their success appears to have been more complete than elsewhere; and if to these investigations we join the researches of Laplace concerning the tides, we shall have the principal important applications hitherto made of the general equations upon which the determination of this kind of motion depends.

In an Appendix to the Actiniæ of the Challenger Expedition, R. Hertwig. 1882, described a peculiar genus, Porponia, with two species, P. elongata and P. robusta, which he characterises in the following manner: “Actiniarien (Hexactinien?) mit 2 Schlundrinnen ohne Ringmuskel, mit dünnwandigen Tentakeln, deren Basen auf der äusseren Seite durch spangenförmige Verlängerungen des Mauerblatts gestützt werden.” Partly owing to the badly preserved material, however, he did not venture to indicate definitely its systematic position, though he considered it conceivable that it represented a transitional form between the Zoanthidæ and the true Actiniæ, or Hexactiniæ.

An onychophoran-like fossil animal, Paucipodia inermis gen. et sp. nov., is described from the Lower Cambrian Chengjiang lagerstatte in Yunnan, China. The animal was soft-bodied, and possessed six pairs of unjointed legs, each having two claws distally. The body was finely annulated, lacked trunk plates, and apparently terminated posteriorly with the last leg pair, without preserved evidence of a posterior trunk extension. Paucipodia widens the morphological range hitherto known in Cambrian lobopodians, notably regarding leg number and presence or absence of plates. Its morphology also provides support for the recently suggested anteroposterior orientation of Hallucigenia and Microdictyon.

Establishing the magnitude and frequency of floods within upland catchments on the basis of short-term gauged runoff records is crucially dependent upon the extent to which the record is truly representative. In the case of the River Dee, upstream of Crathie in Aberdeenshire, gauged discharge records are limited in length. Although the middle Dee has been gauged since 1929, the gauge within the upper catchment has only ten years of record. Thus, reliable estimates of the return intervals of extreme floods for this part of the Dee can only be obtained by using a variety of historical sources to extend the flood series.

Long-term rainfall records, where available, provide a valuable independent check on the reconstructed flood series. Such rainfall records, when analysed in terms of the magnitude, frequency and duration of major events, should, in general terms, correspond with the flood series. In this paper, the recurrence interval of extreme rainfalls of varying magnitude and duration in upper Deeside is estimated by extreme value analysis of the annual maximum series. The frequency of rainfall events above varying thresholds is also assessed. The existence of climatic fluctuations giving highly variable recurrence intervals for rainfall events of the same magnitude is demonstrated. Finally, the seasonality of frequent flood-producing storms is analysed. Patterns observed within the rainfall record are compared with those previously established within the historic flood series to substantiate and augment the flood record.

It is possible, that the following observations may contain little that is new to those who are familiarly acquainted with the details of the science of Hydrostatics. But as I have not met with any remarks on the subject, in the course of my limited reading, the experiments which were performed, and the conclusions to which they lead, are here submitted to the consideration of the Royal Society.

On 17 July 1983 heavy rainfall resulted in a flash-flood in the headwaters of the West Grain, a small stream tributary to the River Wear in the northern Pennines. Associated with the flood was a series of three boulder-lobes. The morphology of these lobes and the associated sediment facies are described and used to estimate the hydro-dynamic mode of transport and deposition. Estimates of the shear-strength and viscosity are consistent with the initial conclusion (based on the sedimentology) that the deposits represent low-viscosity debris-flows. The boulder snouts moved as inertial grain-flows with an associated pebbly-core exhibiting a degree of matrix strength imparted by intergranular friction. A degree of reworking of the upper surface of the core by fluidal flow during core motion and immediately upon deposition was also identified. The full sedimentary sequence therefore represents debris-flow core deposits subject to low dispersive pressure evolving into fluidal debris-torrent deposits.

A new early tetrapod, Mesanerpeton woodi gen. et sp. nov., collected by Stan Wood from the Ballagan Formation, Tournaisian CM palynozone, at Willie's Hole, Scottish Borders, is described. It includes vertebrae like those of Crassigyrinus, with poorly developed neural arches, a well ossified ulna with a large olecranon, and a humerus that is structurally intermediate between the pleisiomorphic condition of Devonian taxa and that of all later forms. A comparative analysis of this new material and other tetrapodomorph humeri revealed how an increase in humeral torsion transformed the course of the brachial artery and median nerve through the bone, from an entirely ventral path to one in which the blood vessel and nerve passed through the entepicondyle from the dorsal to the ventral surface. Increasing humeral torsion is suggested to improve walking in early tetrapods by potentially contributing to an increase in stride length, and is one of a number of changes to limb morphology during the Early Carboniferous that led to the development of terrestrial locomotion.

The geographical area embraced in the present memoir forms a well-marked basin traversed along its centre by the estuary of the Forth. It is bounded on the north by the chain of the Ochil Hills, on the south by the range of the Pentland and Lammermuir uplands. Towards the west it joins along a low watershed the basin of the Clyde, while eastwards it dips under the waters of the North Sea. Within this defined space the Carboniferous rocks occupy what may be described as one great synclinal trough, varied by innumerable smaller synclines and anticlines. Save where cut out by powerful dislocations, their lower members rise up along the margins of the basin, while their highest portions cover a smaller area in the centre. The older formations forming the northern and southern boundaries of the area belong chiefly to the Lower Old Red Sandstone, in the Lammermuir district to the Lower Silurian. The Carboniferous rocks everywhere rest upon them unconformably.

The problems on which we were engaged in the preceding Memoir were the following:—1°, The complete determination of the velocity of transmission of a wave in a fluid of any depth, provided the depth is uniform throughout; 2°, an application of the hypothesis of parallel sections to the problem in its more complicated form, in which the depth is variable in the direction of the breadth of the canal; 3°, The investigation of the motion of a solitary wave. We propose in the following pages to continue the same subjects, and to add the more difficult problem of initial motion.

Dividing and non-dividing nuclei in the hyphæ of M. androsaceus and M. rotula, grown by means of agar- and cellophane-film techniques, were examined alive with phase contrast and also after various fixation and staining procedures. The division was compared with that of the nuclei found in the ultimate clamp connection, i.e. that found, associated with the developing basidium, and with the divisions of the single diploid nucleus in the mature basidium. The end products of all the hyphal divisions are the same as in organisms having a conventional mitosis but some of the steps by which this is achieved are unusual, notably the arrangement of the chromatin as a figure of eight, the twisting of one of the loops so formed above the other to create two rings and the opening of these rings in such a way that the two rods which, ultimately separate each correspond with the chromosome complement of a daughter nucleus. The first division of the diploid nucleus in the basidium is noteworthy for the linking together, in late prophase, of the four chromosomes. This division is followed by a distinct interphase in which nucleoli reappear. The second division shares the peculiarities of the division in the ultimate clamp.

A new chasmataspid (Chelicerata, Chasmataspida) is described as Forfarella mitchelli gen. et sp. nov. from the Lower Devonian of Scotland. This species is problematic in that it was catalogued under the name Forfarella mitchelli Waterston (no date), but was never formally described. Furthermore, its type locality is uncertain. Chasmataspids are a poorly known taxon within Chelicerata which appear to be closely related to eurypterids. F. mitchelli is only the fourth chasmataspid species to be described. Though poorly preserved, it shows affinities with other Devonian chasmataspids and supports the hypothesis that this group may have been more geographically widespread in the Devonian than has previously been recognised.

There are in the Kidston Collection of Fossil Plant Slides sections of four specimens of Lepidodendroid stems, from different Scottish localities in the Carboniferous Limestone Series, which were grouped together by the late Dr Kidston as “Lepidodendron Langi n.sp.” The specimens may be referred to as Nos. 1—4, and the various localities and the numbers of the slides by which the specimens are represented in the Kidston Collection are enumerated here for convenience of reference.

The coast of Northern Trotternish has long attracted the attention of geologists for two reasons, the first being the intermittent exposures of highly fossiliferous Jurassic strata preserved below the great Tertiary lava plateau; and the second, the striking columnar sills of igneous rock which have been intruded into these Mesozoic beds. Intrusive phenomena unparalleled in Britain may be observed (preferably from the sea) from Holm to Staffin Bay, and in slightly less perfect form round the Aird to Duntulm and Camas Mòr.

The Middle Jurassic is a poorly sampled time interval for non-pelagic neosuchian crocodyliforms, which obscures our understanding of the origin and early evolution of major clades. Here we report a lower jaw from the Middle Jurassic (Bathonian) Duntulm Formation of the Isle of Skye, Scotland, UK, which consists of an isolated and incomplete left dentary and part of the splenial. Morphologically, the Skye specimen closely resembles the Cretaceous neosuchians Pachycheilosuchus and Pietraroiasuchus, in having a proportionally short mandibular symphysis, shallow dentary alveoli and inferred weakly heterodont dentition. It differs from other crocodyliforms in that the Meckelian canal is dorsoventrally expanded posterior to the mandibular symphysis and drastically constricted at the 7th alveolus. The new specimen, together with the presence of Theriosuchus sp. from the Valtos Formation and indeterminate neosuchians from the Kilmaluag Formation, indicates the presence of a previously unrecognised, diverse crocodyliform fauna in the Middle Jurassic of Skye, and Europe more generally. Small-bodied neosuchians were present, and ecologically and taxonomically diverse, in nearshore environments in the Middle Jurassic of the UK.

Fifty six sediment cores were collected along a 100 km longitudinal transect of the Thames estuary. Total Hg ranged from 0.01 to 12.07 mg/kg, with a mean of 2.10 mg/kg (n=351). Concentrations of the toxic metal decreased downstream from London to the outer estuary and were positively correlated to total organic carbon (TOC) content. Many Hg profiles showed a clear rise, peak and fall, reflecting changing anthropogenic input through time. Surface concentrations averaged 1.27 mg/kg, confirming the effectiveness of recent environmental legislation and improved river management. Sediments at >40 cm depth from London reaches of the river (Waterloo Bridge, Cuckolds Point (Rotherhithe), Butlers Wharf (Tower Bridge), Millwall, Deptford and Millennium Dome) were highly contaminated, with levels of Hg of >7 mg/kg. The outer Thames had lower Hg, with the exception of Rainham, Crossness and Cliffe. Benchmarking against UK guidelines for the disposal of dredged material revealed that 88 samples from 21 sites exceeded the 3 mg/kg criteria (unsuitable for disposal at sea); 173 fell between 0.3 and 3 mg/kg (further assessment required); and 90 were of no concern. Using Hg as a generic pollution marker, the tidal Thames is one of the world's most contaminated river–estuarine sediment systems.

Several granites and basement gneisses along the southern margin of the Siberian Craton were sampled to obtain precise age constrains and compositional isotopic data. The analysed granite plutons are interpreted to have been emplaced between 1880 and 1850 Ma, and are related to Palaeoproterozoic collisional and post-collisional events. Pb-Pb whole data of a granulite (1884 ± 26 Ma) and a two mica granite (1821 ± 29 Ma) constrain these U-Pb single zircon ages. Sr, Nd and Pb-Pb isotope data reveal the crustal origin of the investigated rocks and the reworking of Archaean material. Nevertheless, a minor influence of a mantle component is still visible in the Pb isotopes. Geodynamically, the magmatic and metamorphic ages in the Kitoy area are linked to several Early Proterozoic events along the southern margin of the Siberian Craton. Since these events are all older than the assembly of Rodinia (about 1·4 Ga ago) the collisional processes are linked to the consolidation of the Siberian Craton itself in Early Proterozoic times.

Significant new material of Late Devonian Gogo Formation fish fossils is still surfacing. Collecting in the past decade has uncovered the first Gogo shark fossils (Gogoselachus plus another new undescribed taxon), the first acanthodian (Halmacanthodes ahlbergi), the first coelacanth, as well as the first placoderm embryos. Recent studies have elucidated the nature of placoderm claspers, pelvic girdles, synarcuals and embryos, the structure of their teeth, a description of well-preserved muscles in placoderms, and how muscles attach to bones. Molecular biomarkers have also been identified in Gogo fossils. There are now five basal ray-fin fishes in the fauna, including one undescribed new taxon. The lungfish fauna from Gogo is the most diverse known for any Devonian site, with 10 genera and 12 species. The dermal skeleton and endocast of the dipterid Rhinodipterus kimberleyensis have been described in detail from CT scans; and the ontogenetic stages of neurocranium formation in Griphognathus. New specimens of the tetrapodomorph fish Gogonasus andrewsae have shed further light on its endocranium, pectoral girdle and fin. Through their exceptional preservation of both hard and varied kinds of soft tissues, the Gogo fishes remain crucial for resolving key debates on the diversification, physiology, biomechanics and phylogenetic relationships of early gnathostomes.

Locally abundant and diverse brachiopod faunas, associated with unstable outer shelf and slope environments, occur throughout the Barr and Ardmillan groups (middle Llanvirn–upper Ashgill) in the Girvan district of SW Scotland. A dataset of 350 brachiopod species from 30 horizons through the Middle–Upper Ordovician succession forms the basis for a description of brachiopod diversity through the succession and comparison with global patterns and trends through this time interval. The Middle Ordovician Barr Group incorporates shallow water carbonate and clastic facies, characterised by Valcourea confinis, with deeper-water facies. The trilobite-dominated Albany Group preserves outer shelf biofacies. Deep-water facies occur in the Balclatchie Formation of the lower Ardmillan Group, including an early occurrence of a Foliomena-type species. High diversity brachiopod faunas occur in clastic facies, though many of the biofacies have a transported component to them. Representatives of the deep-water Foliomena fauna occur intermittently throughout the Upper Ardmillan Group, appearing in both the Whitehouse and Drummuck subgroups. This distinctive assemblage of small, thin-shelled brachiopods, including Dedzetina, Christiania, Cyclospira and Foliomena itself, is interbedded with a variety of other less cosmopolitan deep-water assemblages, including the Onniella–Skenidioides and Lingulella–Trimurellina associations. Shallower-water environments in the middle Ashgill Lower Drummuck Subgroup hosted the Fardenia–Eopholidostrophia association in sands, and the Christiania–Leptaena association in muds and silts. The remarkable Lady Burn Starfish Beds in the upper part of the group contain a variety of brachiopod-dominated assemblages, including the Eochonetes and Plaesiomys–Schizophorella associations, transported from various shelf locations, within a very diverse mid Ashgill biota. The upper Ashgill High Mains Formation contains abundant elements of the terminal Ordovician Hirnantia fauna, including Eostropheodonta, Hindella and Hirnantia itself, but also some taxa more typical of the Laurentian Edgewood Province. As a whole, the changing brachiopod biodiversity biofacies reflect environmental fluctuations, on this part of the Laurentian margin, driven by mainly eustatic and tectonic events against a background of global biotic radiation.

Pegmatites at the East Kemptville Sn-Zn-Cu-Ag deposit occur within a F- and P-rich, 370 Ma topaz-muscovite leucogranite, the most evolved phase of the chemically zoned Davis Lake Pluton. Structural observations and geochronology indicate that the leucogranite intruded into an active shear/fault zone environment. Pegmatites are preferentially located near the roof zone of the intrusion and include: (1) quartz-feldspar pods (≤ 1–2 m) aligned parallel to a foliation in the leucogranite. Such pegmatites have marginal aplites or may be cored by aplites; (2) aplite-pegmatite zones with well-developed crenulate and unidirectional solidification textures; and (3) muscovite-bordered miarolitic cavities lined with quartz-feldspar ± cassiterite. Associated with areas of pegmatites are irregular- to cuspate-shaped zones enriched in muscovite. Mineralogically the pegmatites are simple, consisting of clear to black quartz, albite, microcline perthite and muscovite; topaz may be enriched in aplites coring pegmatites and coarse euhedral cassiterite is rare.

Chemically the leucogranites marginal to pegmatites are similar to the host leucogranite, but some aphanitic felsic dykes indicate extreme differentiation, as reflected by REE depletion and P-enrichment. Enrichment of pegmatitic feldspar in P2O5 (to 1 wt. %) indicates that melts contained 2–3 wt. % P2O5, whereas muscovite chemistry (to 5 wt. % F) reflects the F-rich nature of the melt. Trace and REE contents of pegmatitic feldspars are consistent with local segregation of volatile-rich melts to form pegmatites rather than extreme crystal-chemical fractionation.

Fluid inclusion studies of pegmatitic quartz and cassiterite indicate the presence of a highly saline brine (40 wt. % eq. NaCl; Na > K > Fe > Mn > Ca > Sr) of magmatic origin. Isochores modelled for a 40 wt. % eq. NaCl fluid constrain pegmatite formation at 550–600°C, thus the depressed solidus is consistent with the volatile-rich (F, P, H2O) nature of the melt. Stable isotopes demonstrate that a magmatic fluid (δ18OH2O = +5·5 to +10‰, δDH2O = −33 to −41‰ for 450–500°C) equilibrated with the pegmatites and the system cooled abruptly at c. 425°C.

The low volume of pegmatite at East Kemptville suggests that the melt was not near volatile saturation, instead pegmatite generation is interpreted to have resulted from rapid decompression related to the active shear zone setting of the granite. Although feldspar chemistry reflects a local segregation model, the chemistry of aphanitic dyke rocks indicates that the leucogranite did evolve into a more fractionated melt. The local presence of cassiterite in pegmatites and miarolitic cavities indicates that locally, saturation of Sn occurred, but not throughout the EKL where elevated Sn contents are attributed to infiltration of mineralising fluids (i.e. deuteric alteration).

The Kidston Collection of fossil plant slides in the Botany Department of the University of Glasgow contains a number of sections of a very notable stem labelled “Lepidodendron textum, Kidston, n.sp.” No mention is made of this species in any of Dr Kidston's publications, but the correspondence relevant to the Collection indicates the history of the slides. This may be briefly summarised.

As early as 1883, Dr Kidston had received from Mr J. Coutts two sections (Nos. 51 and 52) of this stem, which had been collected by the latter at East Kilbride, Lanarkshire, Scotland, from the Carboniferous Limestone Series of the Calderwood Beds (Hosie Limestone) in the Lower Limestone Group. Dr Kidston postponed description of this stem till he had better sections at his disposal; the specimen, however, was lost, and it was not till many years later that he rediscovered it in Dr John Young's collection in the Glasgow Municipal Museum, and had more sections cut from it (Nos. 1144–1153). No manuscript notes of Dr Kidston's descriptive of these slides have been found, with the exception of a pencilled reference in his manuscript slide catalogue, opposite Nos. 51 and 52, to the “foliar bundles—there is an appearance as if there was a development of secondary xylem, whereas the axial bundle has no secondary wood.”